A method and system for simulating the transport and deposition of microplastics in turbidity currents

Abstract

The application relates to the technical field of computer simulation, and discloses a turbidity current micro-plastic transport and deposition simulation method and system, which collects three-dimensional shape data and static water stable settlement basic data of micro-plastic particles, obtains geometric data, stable settlement speed and shape characterization parameters of the micro-plastic particles, constructs a complex shape micro-plastic drag force model, establishes a turbidity current fluid domain and a particle domain, solves a fluid phase and a particle phase, obtains fluid field data, particle volume fraction and particle momentum exchange data through particle volume fraction diffusion mapping and fluid momentum back-diffusion processing, calculates fluid action on the particles, particle contact response and flexible deformation state, and obtains deposition position, burial depth and inter-particle force chain data, and performs settlement benchmark verification, water tank working condition verification and parameter sensitivity analysis. Through combination of the complex shape drag force model, the particle volume fraction diffusion mapping and the particle node model, the application improves simulation accuracy and stability.

Description

Technical Field

[0001] This invention relates to the field of computer simulation technology, specifically to a method and system for simulating the transport and deposition of microplastics in turbidity streams. Background Technology

[0002] Currently, microplastic particles are widely present in estuarine, nearshore, and deep-water sedimentary environments. Turbidity currents cause resuspension, transport, collision, deposition, and burial of microplastic particles. Due to the fragmented, fibrous, and film-like morphologies of microplastic particles, their settling velocities, stress states, and contact behaviors with sediment particles vary. Numerical simulation analysis of the movement of microplastic particles in turbidity currents has become a technical means to study their spatial distribution and depositional locations.

[0003] For the microplastic transport and deposition process in turbidity streams, existing simulation methods typically establish fluid and particle computational domains, using computational fluid dynamics (CFD) to solve for the fluid velocity, pressure, and concentration fields, and employing the discrete element method (DEM) to update particle position, velocity, and contact state. The drag force on the particles is usually calculated based on the particle Reynolds number and characteristic particle size, and the volume occupied by the particles and momentum source terms are mapped according to the mesh in which the particles are located. After completing the data exchange between the fluid and particle phases, the transport distance and deposition location are statistically determined based on the particle trajectory and the contact state at the bed surface.

[0004] Existing methods still have limitations in handling complex-shaped microplastic particles. When calculating drag force using spherical particle relationships or single characteristic dimensions, it is difficult to simultaneously reflect the differences in principal axis dimensions, surface area, and projected profiles between fragmented and fibrous microplastic particles. The concentrated distribution of particle-occupied volume and momentum source terms to a single fluid grid cell can easily lead to local fluctuations in volume fraction and fluid momentum within the particle's neighborhood. Furthermore, treating fibrous, fragmented, and film-like microplastic particles as rigid particles cannot describe the bending and torsional states during particle collisions, and it is also difficult to incorporate flexible deformation, interparticle force chains, deposition location, and burial depth into the same verification process.

[0005] Therefore, the present invention provides a method and system for simulating microplastic transport and deposition in turbidity streams to address the shortcomings of the prior art. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method and system for simulating microplastic transport and deposition in turbidity currents. It solves the problems in existing simulations of microplastic transport and deposition in turbidity currents, such as the difficulty in reflecting the sedimentation differences of complex-shaped microplastic particles due to the drag force relationship of spherical particles, the tendency for local numerical fluctuations to occur in the volume fraction mapping and momentum exchange between Lagrange particles and Eulerian grids, the difficulty in characterizing the flexible deformation of fibrous and fragmented microplastic particles by rigid particle models, and the lack of unified correlation between model validation data.

[0007] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for simulating the transport and deposition of microplastics in turbidity streams, employing the following technical solution: A method for simulating microplastic transport and deposition in turbidity streams includes the following steps: Three-dimensional morphological data and static water stable sedimentation baseline data of microplastic particles were collected to obtain geometric data, stable sedimentation velocity and morphological characterization parameters of microplastic particles. A drag force model for complex-shaped microplastics was constructed based on stable settling velocity and morphological characterization parameters, and drag force model parameters were obtained. Based on the geometric data of microplastic particles and the parameters of the drag force model, the turbid fluid domain and particle domain are established, the fluid phase and particle phase are solved, and the fluid field data, particle volume fraction and particle momentum exchange data are obtained by particle volume fraction diffusion mapping and fluid momentum back diffusion processing. Based on the geometric data, fluid field data, particle volume fraction and particle momentum exchange data of microplastic particles, the fluid action and flexible deformation state of the particles are calculated, as well as the particle contact response, to obtain the flexible deformation state, deposition location, burial depth and interparticle force chain data. Based on stable settling velocity, fluid field data, flexible deformation state, deposition location, burial depth, and interparticle force chain data, settling benchmark verification, flume condition verification, and parameter sensitivity analysis were performed to generate transport-deposition response data.

[0008] By adopting the above technical solution, the three-dimensional morphology data of microplastic particles, the basic data of static water stable sedimentation, the parameters of the drag force model, the fluid field data, the particle contact data, and the sedimentation and burial data are sequentially correlated. This allows the calculation of drag force for complex shapes, the two-way fluid-structure interaction calculation, the flexible deformation calculation, and the model verification to use a consistent particle data basis, thereby improving the comparability and accuracy of sedimentation, transport, and deposition results of microplastic particles of different shapes.

[0009] Preferably, microplastic particles are classified into fragmented microplastic particles, fibrous microplastic particles, thin film microplastic particles, and real microplastic samples, and particle labels are assigned to the microplastic particles; three-dimensional voxel data, three-dimensional point cloud data, or three-dimensional surface mesh data are collected using an X-ray three-dimensional microscope, and background removal, particle region segmentation, pore filling, surface reconstruction, and coordinate unification are performed on the collected data to obtain a closed three-dimensional surface.

[0010] Based on the closed three-dimensional surface, the major axis, intermediate axis, and minor axis of the fragmented microplastic particles are determined, the axial length and cross-sectional diameter of the fibrous microplastic particles are determined, and the particle volume, actual surface area, equivalent diameter, projected area, equivalent area diameter, and two-dimensional projected profile perimeter are calculated to form the geometric data of the microplastic particles.

[0011] By adopting the above technical solution, the principal axis dimensions, volume, surface area and projection geometric parameters can be obtained uniformly using a closed three-dimensional surface, reducing the parameter deviation caused by the inability of two-dimensional projection data to fully characterize the three-dimensional morphology of complex particles.

[0012] Preferably, a single microplastic particle is released from the top of the sedimentation column through a particle release component, sedimentation images are continuously acquired and the particle center position and particle posture are determined; a corresponding sequence of sedimentation distance and sedimentation time is generated based on the particle center position and acquisition time.

[0013] A stable settlement interval is determined when the change in settlement distance per unit time between adjacent time intervals does not exceed the stability threshold. The stable settlement velocity is then determined based on the settlement distance and settlement time within this interval. The stability threshold is determined based on the spatial and temporal resolution of the high-speed camera and remains constant within the same experimental batch.

[0014] By adopting the above technical solution, the data range corresponding to initial acceleration, sudden changes in particle posture, and image recognition errors can be eliminated, so that the stable settling velocity comes from a continuous and stable settling process.

[0015] Preferably, the Aschenbrenner coefficient, Corey coefficient, Janke coefficient, slenderness, flatness, sphericity, roundness, Delino coefficient, and aspect ratio are calculated based on the geometric data of microplastic particles to form morphological characterization parameters, and the morphological characterization parameters are associated with particle identification, particle morphology category, particle density, and stable settling velocity and stored.

[0016] The Aschenbrenner coefficient for fragmented microplastic particles is determined by the product of the major axis length and the minor axis length and the square of the intermediate axis length; the Aschenbrenner coefficient for fibrous microplastic particles is determined by the ratio of axial length to cross-sectional diameter.

[0017] The Corey coefficient of fragmented microplastic particles is determined based on the ratio of the minor axis length to the combined dimensions of the major axis length and the intermediate axis length; the Corey coefficient of fibrous microplastic particles is determined based on the ratio of the cross-sectional diameter to the combined dimensions of the axial length and the cross-sectional diameter.

[0018] The Janke coefficient of fragmented microplastic particles is determined based on the ratio of the minor axis length to the root mean square scale of the three principal axis dimensions. The elongation of fragmented microplastic particles is determined based on the ratio of the intermediate axis length to the major axis length, the flatness is determined based on the ratio of the minor axis length to the intermediate axis length, and the aspect ratio is determined based on the ratio of the major axis length to the minor axis length.

[0019] The slenderness of fibrous microplastic particles is determined by the ratio of cross-sectional diameter to axial length, the flatness is determined by the cross-sectional dimensions, and the aspect ratio is determined by the ratio of axial length to cross-sectional diameter.

[0020] Sphericity is determined based on the relationship between the actual surface area of ​​microplastic particles and the surface area of ​​a sphere of the same volume, or based on the relationship between the equivalent diameter and the equivalent area diameter; circularity is determined based on the relationship between the perimeter of the two-dimensional projected profile and the circumference of a circle with an equal projected area; the Delino coefficient is determined based on the relationship between sphericity and circularity.

[0021] By adopting the above technical solution, the non-spherical nature of microplastic particles is characterized by the main axis size, surface area and projected profile, enabling the drag force model to accurately distinguish the morphological differences between fragmented microplastic particles and fibrous microplastic particles.

[0022] Preferably, the particle Reynolds number is determined based on the stable settling velocity, particle density, fluid density, fluid dynamic viscosity, and particle characteristic size, wherein the particle characteristic size of fragmented microplastic particles is the equivalent diameter, and the particle characteristic size of fibrous microplastic particles is the characteristic size corresponding to the dragging direction.

[0023] Particle Reynolds number, morphological characterization parameters, and steady-state settling velocity were grouped according to particle morphology. The Levenburg-Marquardt algorithm was used to perform nonlinear regression to establish fragment drag force models and fiber drag force models, respectively. The drag force model parameters were verified and calibrated using the steady-state settling velocity of real microplastic samples.

[0024] Nonlinear regression uses the residual between the predicted stable settlement velocity and the experimental stable settlement velocity as the target data, and reduces the sum of squared residuals by adjusting the regression parameters. Regression stopping conditions include the relative increment of parameters reaching the parameter convergence threshold, the relative change of the objective function reaching the target convergence threshold, or the number of iterations reaching the iteration limit.

[0025] By adopting the above technical solution, the drag force model simultaneously incorporates particle Reynolds number and morphology characterization parameters, and fits them separately according to particle morphology categories. This can effectively reduce the settling velocity error generated when only using the relationship between spherical particles to calculate complex-shaped microplastic particles.

[0026] Preferably, an Eulerian grid is used to discretize the turbidity fluid domain, and the turbidity inlet, fluid outlet, top boundary, sidewall boundary and bed boundary are set; sediment particles and microplastic particles are established in the particle domain, and the initial position, initial translational velocity, initial angular velocity, initial attitude, particle density, particle size, particle morphology type and contact properties are set.

[0027] The fluid phase control equations are discretized using the finite volume method, the velocity and pressure fields are solved using the phase-coupled semi-implicit pressure correlation equation algorithm, the turbulence parameter field is updated using the renormalized group k-ω turbulence model, and the particle phase is solved using the discrete element method.

[0028] By adopting the above technical solution, the fluid phase and particle phase can be updated synchronously in the same computational domain, so that the movement of turbid fluid, sediment particles and microplastic particles maintain a high degree of temporal and spatial coupling.

[0029] Preferably, the fluid grid cell where the center of each particle is located is determined, the volume occupied by the particle is written into the corresponding fluid grid cell, and diffused to the adjacent fluid grid cells according to the grid adjacency relationship and spatial distance.

[0030] The particle volume fraction is determined based on the volume occupied by particles in each fluid grid cell and the volume of the fluid grid cell, while maintaining the total volume of a single particle before and after mapping as well as the total volume of all particles before and after mapping.

[0031] The particle momentum source term is subjected to fluid reverse diffusion processing based on the spatial weights used in the volume diffusion process. The particle momentum influence is distributed to the grid where the particle is located and the adjacent grids, while keeping the total momentum exchange between the particle phase and the fluid phase constant.

[0032] By adopting the above technical solution, particle volume fraction mapping and particle momentum exchange use corresponding neighborhood relationships and spatial weights, which greatly reduces the local numerical fluctuations caused by particles being concentrated in a single fluid grid cell while maintaining the conservation of total particle volume and total interphase momentum.

[0033] Preferably, fluid velocity, fluid pressure, fluid concentration, and turbulence parameters are read from the fluid field data to obtain the fluid density, and the fluid velocity, fluid pressure, fluid density, fluid concentration, and turbulence parameters are interpolated to the particle location.

[0034] A complex-morphology microplastic drag force model was used to calculate the drag force, lift force, pressure gradient force, and virtual mass force. The particle-vortex interaction time was determined based on the smaller of the vortex duration and particle transport time. During the particle-vortex interaction time, the current vortex parameters were maintained on the particles. After the interaction time ended, the turbulence parameters at the particle's location were re-read.

[0035] By adopting the above technical solution, it is possible to calculate the fluid action on the particle according to the fluid parameters at the actual location of the particle, and to scientifically limit the duration of the continuous action of the same turbulent vortex on the particle.

[0036] Preferably, fibrous microplastic particles are constructed by connecting multiple spherical cylindrical units, and fragmented microplastic particles and film-like microplastic particles are constructed by connecting multiple rounded triangular prism units.

[0037] At the connection nodes, the nodal linear elastic action, nodal bending moment, nodal torsional moment, and nodal damping are calculated to form nodal action. The position and orientation of each connection element are updated based on the nodal resultant force and nodal resultant moment to obtain the flexible deformation state.

[0038] The number of connecting units is determined based on the upper limit of the three-dimensional morphological discretization error. When the rate of change of the total particle volume, the rate of change of the particle external surface area, and the rate of change of the principal axis size before and after increasing the number of connecting units are all no greater than the upper limit of the three-dimensional morphological discretization error, the increase in the number of connecting units is stopped.

[0039] By adopting the above technical solution, the particle node model can realistically characterize the bending and torsion states of fibrous microplastic particles, fragmented microplastic particles, and thin film microplastic particles under the action of turbidity and collision.

[0040] Preferably, the contact relationships between sediment particles, between sediment particles and microplastic particles, between microplastic particles, and between particles and the substrate are detected. The normal contact response is calculated using the Hertz spring-damping model, and the tangential contact response is calculated using the Mindlin-Deresiewicz tangential contact model.

[0041] The fluid action, particle contact response, gravity action, and node action on the particles are combined to update the particle translational velocity, angular velocity, spatial position, and attitude, and the force chain data between particles are obtained based on the contact relationship.

[0042] When a particle is in continuous contact with the substrate and its velocity does not exceed the deposition rate threshold, it is determined that the particle is in a depositional state. When a particle is covered by sediment particles with a thickness reaching the particle burial determination depth, it is determined that the particle is in a burial state. The deposition rate threshold is determined based on the ratio of particle position measurement resolution to particle time step, and the particle burial determination depth is determined based on the minor axis dimension or cross-sectional diameter of the target particle.

[0043] By adopting the above technical solutions, it is possible to scientifically distinguish between suspended state, near-bed transport state, sedimentation state and burial state based on particle movement, contact and covering state, and accurately obtain the sedimentation location and burial depth.

[0044] Preferably, a static water calculation domain consistent with the static water settlement experiment is established, the simulated stable settlement velocity is compared with the experimental stable settlement velocity, and the mean absolute error, coefficient of determination, and root mean square error are calculated; when the mean absolute error is not greater than 1.00 mm / s, the coefficient of determination is not less than 0.90, and the root mean square error is not greater than 1.20 mm / s, the settlement benchmark verification is deemed successful.

[0045] A numerical flume matching the experimental conditions of the flume model was established. The turbidity velocity profile, turbidity concentration profile, and spatial distribution of microplastic particles were compared at the same measurement location and at the same evolution time. The velocity profile error, concentration profile error, and microplastic spatial distribution error were calculated.

[0046] By changing the initial conditions of turbidity flow, initial conditions of particles, particle contact properties, and discrete settings of particle nodes, the various variable parameter conditions are compared with the baseline conditions to form transport and deposition response data.

[0047] By adopting the above technical solutions, the settlement benchmark verification, flume working condition verification, and parameter sensitivity analysis comprehensively evaluate the drag force model, fluid-structure interaction numerical model, and the response of the main control factors, forming a highly reliable model verification system that is interconnected.

[0048] Secondly, this invention provides a microplastic transport and deposition simulation system in turbidity streams, employing the following technical solution: A microplastic transport and deposition simulation system in turbidity currents is provided for performing the aforementioned microplastic transport and deposition simulation method in turbidity currents. The system includes a sedimentation data acquisition module, a morphological parameter construction module, a fluid-structure interaction calculation module, a transport and deposition analysis module, and a model verification and evaluation module.

[0049] The sedimentation data acquisition module is used to collect basic data on the static water stable sedimentation of microplastic particles, and obtain the particle center position, particle posture, sedimentation distance, sedimentation time, and stable sedimentation velocity.

[0050] The morphological parameter construction module is used to collect three-dimensional morphological data of microplastic particles, obtain geometric data of microplastic particles, and calculate morphological characterization parameters based on the geometric data of microplastic particles; the morphological parameter construction module is also used to construct a drag force model of complex-shaped microplastics based on the stable settling velocity and the morphological characterization parameters, and obtain drag force model parameters.

[0051] The fluid-structure interaction calculation module is used to establish the turbid fluid domain and particle domain based on the geometric data of microplastic particles and the parameters of the drag force model, solve the fluid phase and particle phase, and obtain fluid field data, particle volume fraction and particle momentum exchange data through particle volume fraction diffusion mapping and fluid momentum back diffusion processing.

[0052] The transport and deposition analysis module is used to calculate the fluid effects and flexible deformation state of particles based on microplastic particle geometry data, fluid field data, particle volume fraction and particle momentum exchange data, as well as to calculate particle contact response, and obtain flexible deformation state, deposition location, burial depth and interparticle force chain data.

[0053] The model validation and evaluation module is used to perform sedimentation benchmark validation, flume condition validation, and parameter sensitivity analysis based on stable sedimentation velocity, fluid field data, flexible deformation state, sedimentation location, burial depth, and interparticle force chain data, thereby generating transport and sedimentation response data.

[0054] By adopting the above technical solution, each functional module is closely connected in the order of generating static water sedimentation data, three-dimensional morphological data of microplastic particles, morphological characterization parameters, drag force model parameters, fluid field data, particle motion data and model verification data, so as to realize continuous and automated calculation of complex morphological microplastic particles from static water sedimentation parameter acquisition, morphological parameter construction, drag force model establishment to turbidity transport and deposition result verification.

[0055] Preferably, the sedimentation data acquisition module is connected to the morphological parameter construction module, and the sedimentation data acquisition module sends particle identification, sample type, sedimentation time, sedimentation distance, particle posture and stable sedimentation velocity to the morphological parameter construction module.

[0056] The morphological parameter construction module is connected to the fluid-structure interaction calculation module. The morphological parameter construction module sends particle morphology type, particle geometry, particle morphology characterization parameters, and drag force model parameters to the fluid-structure interaction calculation module.

[0057] The fluid-structure interaction calculation module is connected to the transport and deposition analysis module. The fluid-structure interaction calculation module sends fluid field data, particle position data, particle velocity data, particle attitude data, particle force data, and particle contact data to the transport and deposition analysis module.

[0058] The transport and sedimentation analysis module is connected to the model validation and evaluation module. The transport and sedimentation analysis module sends the stable sedimentation velocity simulation results, turbidity flow velocity profile, turbidity flow concentration profile, spatial distribution of microplastic particles, sedimentation location, burial depth and interparticle force chain data to the model validation and evaluation module.

[0059] By adopting the above technical solution, each system module is connected by hardware or software through a clear data input and output relationship, so that the data corresponding to particle identification, experimental identification, working condition identification and calculation time can be continuously transmitted and stored in a highly correlated manner.

[0060] Preferably, the microplastic transport and deposition simulation system in turbidity streams is deployed in a computing device that includes a processor, memory, data interface, and display device.

[0061] The memory is used to store three-dimensional morphological data of microplastic particles, sedimentation experiment videos, stable sedimentation velocity data, morphological characterization parameters, computational grid data, fluid initial conditions, fluid boundary conditions, particle initial conditions, particle contact parameters, drag force model parameters, particle state data, and model verification data.

[0062] The processor calls program instructions from memory to perform sedimentation trajectory processing, morphological parameter extraction, nonlinear regression, fluid phase solution, particle phase solution, fluid-structure interaction, transport and deposition analysis, and model verification.

[0063] By adopting the above technical solution, the underlying computing device can automatically call each application module according to a unified data identifier and logical calculation order, and efficiently complete the numerical simulation of the complex morphological microplastic transport and deposition process in turbidity streams.

[0064] This invention provides a method and system for simulating microplastic transport and deposition in turbidity streams. It offers the following advantages: 1. This invention collects three-dimensional morphological data of microplastic particles and basic data on static water stable settling, calculates the Aschenbrenner coefficient, Corey coefficient, Janke coefficient, slenderness, flatness, sphericity, roundness, Delino coefficient, and aspect ratio, and constructs a drag force model for complex-shaped microplastics by combining stable settling velocity. This enables the drag force calculation to reflect the geometric differences of fragmented microplastic particles, fibrous microplastic particles, and other irregularly shaped microplastic particles, thereby improving the accuracy of stable settling velocity and transport trajectory calculations.

[0065] 2. This invention employs particle volume fraction diffusion mapping and fluid momentum back diffusion processing to allocate the volume occupied by particles and the momentum source term of particles to the fluid grid cell where the particles are located and adjacent fluid grid cells, while keeping the total volume of particles and the total momentum exchange between the particle phase and the fluid phase unchanged. This can reduce the local numerical fluctuations caused by the concentrated mapping of particles to a single grid cell and improve the stability of bidirectional coupling calculation between the fluid phase and the particle phase.

[0066] 3. This invention uses a particle node model to construct fibrous microplastic particles, fragmented microplastic particles, and film-like microplastic particles. Combined with the identification of particle contact response, flexible deformation state, deposition state, and burial state, as well as sedimentation benchmark verification, flume condition verification, and parameter sensitivity analysis, it can obtain the deposition location, burial depth, and interparticle force chain data of microplastic particles, providing a calculation basis for analyzing the collision, transport, deposition, and burial processes of microplastic particles in turbidity currents. Attached Figure Description

[0067] Figure 1 This is a framework diagram of the microplastic transport and deposition simulation system in turbidity streams according to the present invention; Figure 2 This is a flowchart of the microplastic transport and deposition simulation method in turbidity streams according to the present invention; Figure 3 This is a flowchart of the process for acquiring microplastic morphology and sedimentation data according to the present invention; Figure 4 Flowchart for constructing the complex-shaped microplastic drag force model of the present invention; Figure 5 A flowchart is established for the numerical framework of fluid-structure interaction in this invention; Figure 6 This is a framework diagram of the numerical model coupling computational fluid dynamics and discrete element method of the present invention; Figure 7 This is a diagram of the particle volume fraction algorithm of the present invention; Figure 8 This is a flowchart of the computational process for the coupling of turbidity transport and deposition in this invention; Figure 9 This is a flowchart of the model validation and parameter sensitivity analysis of the present invention; Figure 10 This is a sedimentation curve diagram of microplastic particles of different morphologies according to the present invention; Figure 11 This is a graph comparing the simulation results with the experimental results of this invention. Detailed Implementation

[0068] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] The microplastic particles in this embodiment include fragmented microplastic particles, fibrous microplastic particles, thin-film microplastic particles, and other irregularly shaped microplastic particles obtained from samples of the target water body. Sediment particles and microplastic particles together constitute the particulate phase, while the liquid carrying the turbidity current constitutes the fluid phase.

[0070] In this embodiment, the computational fluid dynamics-discrete element method (CFD-DEM) coupling is used to simultaneously solve for the motion of the fluid phase and the particle phase. Computational fluid dynamics (CFD) is used to solve for the velocity field, pressure field, concentration field, and turbulence parameter field of the turbid fluid phase. The discrete element method (DEM) is used to solve for the translational, rotational, contact, collision, friction, and flexible deformation processes of sediment particles and microplastic particles.

[0071] This invention provides a microplastic transport and deposition simulation system in turbidity streams, deployed in a computing device comprising a processor, memory, data interface, and display. The memory stores three-dimensional morphological data of microplastic particles, sedimentation experiment videos, stable sedimentation velocity data, computational grid data, initial fluid conditions, fluid boundary conditions, initial particle conditions, particle contact parameters, drag force model parameters, particle state data, and model validation data. The processor calls program instructions from the memory to perform morphological parameter extraction, sedimentation trajectory processing, nonlinear regression, fluid phase solution, particle phase solution, fluid-structure interaction, transport and deposition analysis, and model validation.

[0072] See attached document Figure 1 The present invention provides a microplastic transport and deposition simulation system in turbidity currents, including a sedimentation data acquisition module, a morphological parameter construction module, a fluid-structure interaction calculation module, a transport and deposition analysis module, and a model verification and evaluation module.

[0073] The sedimentation data acquisition module is connected to the morphology parameter construction module, sending particle identification, sample type, sedimentation time, sedimentation distance, particle attitude, and stable sedimentation velocity to the morphology parameter construction module. The morphology parameter construction module is connected to the fluid-structure interaction (FSI) calculation module, sending particle morphology type, particle geometry, particle morphology characterization parameters, and drag force model parameters to the FSI calculation module. The FSI calculation module is connected to the transport and deposition analysis module, sending fluid field data, particle location data, particle velocity data, particle attitude data, particle force data, and particle contact data to the transport and deposition analysis module. The transport and deposition analysis module is connected to the model validation and evaluation module, sending stable sedimentation velocity simulation results, turbidity current velocity profiles, turbidity current concentration profiles, spatial distribution of microplastic particles, sedimentation location, burial depth, and interparticle force chain data to the model validation and evaluation module.

[0074] The sedimentation data acquisition module is used to acquire sedimentation data of microplastic particles of different shapes in still water. The module includes a sedimentation column, a particle release assembly, a high-speed camera, a lens, a Universal Serial Bus (USB) data interface, and a video processing unit. The sedimentation column contains still liquid, the particle release assembly is located at the top of the column, and the high-speed camera and lens are positioned 10 cm above the bottom of the column.

[0075] The particle release assembly delivers microplastic particles into the settling column using a single-particle release method. Under the influence of gravity and fluid resistance, the microplastic particles gradually transition from an initial acceleration state to a stable, uniform descent state. A high-speed camera captures continuous settling footage of the microplastic particles after they enter the bottom observation area and transmits this footage to the video processing unit via a universal serial bus data interface.

[0076] The video processing unit identifies the outlines of microplastic particles according to the time sequence of video frames, determining the particle center position, principal axis direction, and particle orientation in each video frame. Based on the time interval between adjacent video frames and the change in particle center position, the video processing unit generates a data sequence of sedimentation distance over time. When the sedimentation distance per unit time remains stable within a continuous observation interval, the video processing unit defines this observation interval as a stable sedimentation interval and determines the stable sedimentation velocity based on the sedimentation distance and sedimentation time within the stable sedimentation interval.

[0077] The sedimentation data acquisition module establishes sedimentation experiment datasets according to the purposes of model building and model validation. The model building dataset includes 100 sets of sedimentation experiment data for typical fragmented microplastic particles, fibrous microplastic particles, and other typical forms of microplastic particles. The model validation dataset includes 50 sets of real microplastic particle sedimentation experiment data obtained from samples in the target water area. The sedimentation data acquisition module assigns particle identifiers and experiment identifiers to each set of sedimentation experiments and associates the experiment identifiers with microplastic particle type, particle density, particle size, sedimentation video, stable sedimentation range, and stable sedimentation velocity.

[0078] The morphological parameter construction module is used to acquire the three-dimensional structure of microplastic particles and construct morphological characterization parameters corresponding to the particle morphology. The module receives three-dimensional voxel data, three-dimensional point cloud data, or three-dimensional surface mesh data output from an X-ray three-dimensional microscope, and segments and reconstructs the outer surface of the microplastic particles.

[0079] The morphological parameter construction module determines the major axis, intermediate axis, and minor axis of the fragmented microplastic particles based on the reconstructed 3D structure, the axial length and cross-sectional diameter of the fibrous microplastic particles, and the volume, actual surface area, equivalent diameter, projected area, equivalent area diameter, and 2D projected profile perimeter of the microplastic particles. The morphological parameter construction module stores the 3D structural data and the stable settling velocity output by the settling data acquisition module according to the particle identification.

[0080] The morphological parameter construction module calculates the Aschenbrenner coefficient, Corey coefficient, Janke coefficient, slenderness, flatness, sphericity, roundness, Delino coefficient, and aspect ratio based on particle geometry. Fragmented microplastic particles are characterized using a morphological relationship based on their major axis, intermediate axis, and minor axis. Fibrous microplastic particles are characterized using a morphological relationship based on their axial length and cross-sectional diameter.

[0081] The morphological parameter construction module employs the Levenberg-Marquardt algorithm to regress the nonlinear relationship between particle Reynolds number, morphological characteristics, and steady-state settling velocity. The regression process uses 100 sets of typical microplastic particle settling experimental data as model construction data and 50 sets of real microplastic particle settling experimental data as model validation and calibration data. The regression results include drag force model parameters, regression residuals, number of iterations, convergence status, and applicable particle types.

[0082] The fluid-structure interaction (FSI) calculation module is used to establish a two-way coupled computational domain between the turbid fluid phase and the particle phase. The FSI module includes a fluid domain establishment unit, a particle domain establishment unit, a fluid phase solution unit, a particle phase solution unit, a particle volume fraction mapping unit, and a momentum exchange unit.

[0083] The fluid domain creation unit establishes an Eulerian grid based on the geometry of the sedimentation column or flume experimental setup, and sets the turbidity inlet, fluid outlet, top boundary, sidewall boundary, and substrate boundary. The particle domain creation unit sets the initial position, initial velocity, initial orientation, particle density, particle size, particle morphology, and particle contact properties of sediment particles and microplastic particles.

[0084] The fluid phase solution unit uses the Finite Volume Method (FVM) to discretize the fluid phase governing equations and employs the Phase-Coupled Semi-Implicit Method for Pressure-Linked Equations (PC-SIMPLE) to perform coupled calculations of the pressure and velocity fields. The fluid phase solution unit uses the Renormalization Group k-omega turbulence model (RNGk-ω) to calculate the turbulent kinetic energy, turbulent frequencies, and turbulent transport processes in the turbulent flow.

[0085] The particle phase solution unit uses the Hertzian spring-dashpot model to calculate the normal contact response of the particles and the Mindlin-Deresiewicz tangential contact model to calculate the tangential contact response. The particle phase solution unit updates the translational velocity, angular velocity, spatial position, and attitude of the particles based on the fluid interaction, interparticle contact, and bed surface contact.

[0086] The particle volume fraction mapping unit employs a volume diffusion-based Lagrange-Eulerian mapping method to map the volume occupied by each Lagrange particle to its corresponding Eulerian grid, and diffuses the particle volume information to adjacent Eulerian grids. The particle volume fraction mapping unit generates a continuous particle volume fraction field while maintaining the conservation of the total particle volume.

[0087] The momentum exchange unit employs a fluid reverse diffusion method to handle momentum transfer between the particle and fluid phases. The momentum exchange unit transfers the momentum source term corresponding to the force acting on the particle to the mesh containing the particle and adjacent meshes, and performs reverse diffusion recovery according to the spatial weights of the volume diffusion process, so that the fluid velocity and pressure changes in the particle's neighborhood are retained in the computational mesh.

[0088] The transport and deposition analysis module is used to calculate the suspension, transport, diffusion, collision, deposition, and burial processes of microplastic particles in turbidity streams. The module includes a particle-fluid interaction calculation unit, a particle contact calculation unit, a flexibility deformation calculation unit, a particle state identification unit, and a results statistics unit.

[0089] The particle-fluid interaction calculation unit calculates drag force, lift force, pressure gradient force, and virtual mass force, and handles turbulent dispersion based on particle-vortex interaction time. The drag force calculation calls the drag force model output by the morphology parameter construction module, allowing fragmented and fibrous microplastic particles to participate in the calculation according to their corresponding morphology characterization parameters.

[0090] The particle contact calculation unit detects the contact between microplastic particles and sediment particles, the contact between microplastic particles, and the contact between particles and the bed surface. The particle contact calculation unit records the contact initiation time, contact duration, contact normal displacement, contact tangential displacement, normal contact force, tangential contact force, and friction state.

[0091] The flexible deformation calculation unit uses a joint model to construct fibrous microplastic particles, fragmented microplastic particles, and film-like microplastic particles. Fibrous microplastic particles are composed of multiple connected spherical cylindrical elements. Fragmented and film-like microplastic particles are composed of multiple connected rounded triangular prism elements. The number of elements is determined based on the discretization accuracy of the actual particle morphology; increasing the number of elements results in a particle structure with more connection nodes.

[0092] The flexible deformation calculation unit uses a nodal linear elastic model to calculate the forces, moments, bending deformation, and torsional deformation at the connections between adjacent units, and applies nodal damping at the connection nodes. Nodal damping is used to attenuate high-frequency nodal oscillations caused by instantaneous collisions. The particle nodal model updates the position, orientation, and connection state of each unit within each particle time step.

[0093] The particle state identification unit identifies the suspension state, near-bed transport state, bed surface contact state, deposition state, and burial state of particles based on their vertical position, particle velocity, contact state with the bed surface, and contact duration. The results statistics unit outputs particle trajectory, transport distance, diffusion range, deposition location, burial depth, number of collisions, number of frictions, contact duration, and force chain distribution between particles.

[0094] The model validation and evaluation module is used to validate the drag force model, the fluid-structure interaction numerical model, and the transport and deposition calculation results. The module includes a settlement benchmark validation unit, a flume condition validation unit, an error evaluation unit, and a parameter sensitivity analysis unit.

[0095] The sedimentation benchmark verification unit establishes a static water computational domain consistent with the sedimentation experiment conditions. The microplastic particle morphology, particle density, fluid properties, release location, and observation location are set to be consistent with the sedimentation experiment. The simulated sedimentation curve, simulated stable sedimentation velocity, and experimental stable sedimentation velocity are compared.

[0096] The flume operation verification unit established a numerical flume that matched the experimental conditions of the flume model, and selected five typical experimental conditions to perform fluid-structure interaction calculations. The flume operation verification unit extracted turbidity velocity profiles, turbidity concentration profiles, and spatial distribution of microplastic particles at the same measurement locations and evolution times as the flume experiments.

[0097] The error evaluation unit calculates the mean absolute error, coefficient of determination, and root mean square error, and compares the results with evaluation thresholds pre-written into the validation configuration file. These evaluation thresholds are determined before the validation calculation begins and remain unchanged after the calculation. When an evaluation index fails to meet a threshold, the model validation evaluation module marks the corresponding particle sample or the corresponding water tank condition as calibration data and sends the calibration data to the morphological parameter construction module or the fluid-structure interaction calculation module.

[0098] The parameter sensitivity analysis unit modifies the initial conditions of turbidity flow, initial conditions of particles, particle contact properties, and particle node discrete settings to form multiple sets of variable parameter calculation conditions. The parameter sensitivity analysis unit compares the particle transport distance, diffusion range, suspension duration, deposition location, burial depth, and interparticle force chain distribution under different conditions to determine the influence of each main controlling factor on the microplastic transport and deposition results.

[0099] See attached document Figure 2 The present invention provides a method for simulating the transport and deposition of microplastics in turbidity streams, comprising steps S100 to S500.

[0100] Step S100: Collect basic data on the three-dimensional morphology and static water stable settling of microplastics. This is executed through the settling data acquisition module and the morphology parameter construction module to obtain the three-dimensional geometric structure, particle morphology type, stable settling velocity, and morphological characterization parameters of the microplastic particles.

[0101] Step S200: Construct a drag force model for complex-shaped microplastics and complete calibration with real samples. This is performed through the morphology parameter construction module, which establishes the functional relationship between particle Reynolds number, morphology characterization parameters, and drag force coefficient, and verifies and calibrates the drag force model parameters using real microplastic samples.

[0102] Step S300: Establish a fluid-structure interaction numerical framework that considers complex particle morphology and interphase back diffusion. This is executed through the fluid-structure interaction calculation module, which is used to establish the turbid fluid domain and particle domain, solve for the fluid phase and particle phase, and complete the particle volume fraction mapping and momentum exchange between particles and the fluid.

[0103] Step S400 calculates the particle-fluid interaction, particle-contact interaction, and microplastic transport and deposition process. This is performed through the transport and deposition analysis module to calculate the fluid interaction on the particles, particle contact response, flexible deformation of complex-shaped microplastic nodes, and particle deposition and burial state.

[0104] Step S500 involves performing sedimentation benchmark, flume condition verification, and sensitivity analysis of key control parameters. This is performed through the model validation and evaluation module to compare simulation results with experimental results, calculate model evaluation indices, and determine the impact of different key control factors on microplastic transport and deposition results.

[0105] Steps S100 to S500 are executed sequentially according to the data generation order. The microplastic particle geometric data, stable settling velocity, and morphological characterization parameters output from step S100 are used as inputs to step S200. The drag force model parameters output from step S200 are used as inputs to steps S300 and S400. The fluid field data, particle volume fraction, and particle momentum exchange data output from step S300 are used as inputs to step S400. The stable settling velocity simulation results, turbidity flow velocity profile, turbidity concentration profile, spatial distribution of microplastic particles, deposition location, burial depth, and interparticle force chain data output from step S400 are used as inputs to step S500.

[0106] See attached document Figure 3 Step S100 involves collecting basic data on the three-dimensional morphology and static water stability settlement of microplastics. Step S100 is executed through the settlement data acquisition module and the morphology parameter construction module, and includes the following sub-steps.

[0107] Sub-step S101: Complete the classification and coding of microplastic samples and obtain the three-dimensional geometric structure data of the particles. The microplastic samples to be tested were classified into fragmented microplastic particles, fibrous microplastic particles, film-like microplastic particles, and real microplastic samples. Each microplastic particle was assigned a unique particle identifier, which was associated with the sample source category, particle morphology category, and experimental batch.

[0108] Three-dimensional structural data of microplastic particles were acquired using an X-ray three-dimensional microscope. Background removal, particle region segmentation, pore filling, surface reconstruction, and coordinate unification were performed on the 3D structural data to obtain the closed 3D surface of the microplastic particles. The 3D surface meets the sealing requirements for volume and surface area calculations.

[0109] For fragmented microplastic particles, determine the major axis, intermediate axis, and minor axis. For fibrous microplastic particles, determine the axial length and cross-sectional diameter. For thin-film microplastic particles, determine the planar principal axis dimensions and thickness dimensions. Simultaneously calculate the particle volume, actual surface area, equivalent diameter, projected area, equivalent area diameter, and two-dimensional projected profile perimeter.

[0110] Each geometric data point is associated with a particle identifier, and a data integrity check is performed. Samples lacking a 3D closed surface, with broken particle boundaries, or where the measurement area does not completely cover the particle are not written into the model building dataset, and 3D morphology acquisition is re-executed.

[0111] Sub-step S102: Perform a static water sedimentation experiment and extract the stable sedimentation velocity of microplastic particles. A static liquid was added into the sedimentation column, and the liquid temperature and level were kept stable during a single experiment. A high-speed camera and lens were positioned 10 cm above the bottom of the sedimentation column, so that the area being filmed corresponded to the movement range of the microplastic particles after they entered a stable descent state.

[0112] Individual microplastic particles are released from the top of the settling column via a particle release assembly. A high-speed camera continuously captures images of the particles settling over the observation area and transmits these images to a video processing unit. The acquisition time is recorded for each video frame, and the time sequence of the video frames is maintained continuously.

[0113] The video processing unit identifies particle outlines and center positions, forming a sequence of sedimentation distance and sedimentation time. For multiple consecutive time intervals, the unit-time sedimentation distance is calculated. When the change in unit-time sedimentation distance between adjacent time intervals does not exceed a preset stability threshold, the corresponding interval is determined as a stable sedimentation interval.

[0114] The stability threshold is determined before the experiment based on the spatial and temporal resolution of the high-speed camera and remains constant within the same experimental batch. The stability threshold is used to exclude data intervals corresponding to the initial particle acceleration phase, abrupt particle attitude changes, and image recognition errors.

[0115] The stable settlement velocity was determined based on the cumulative settlement distance and cumulative settlement time within the stable settlement interval. A total of 150 sets of settlement experiments were conducted, of which 100 sets of settlement experiments with typical fragmented microplastic particles, fibrous microplastic particles, and other typical forms of microplastic particles were used for drag force model parameter construction, and 50 sets of settlement experiments with real microplastic samples were used for drag force model verification and parameter calibration.

[0116] Sub-step S103: Calculate the morphological characterization parameters of microplastic particles with different shapes and form the model input data. Based on the three-dimensional morphological data, the morphological characterization parameters of fragmented microplastic particles and fibrous microplastic particles were calculated respectively.

[0117] The Aschenbrenner coefficient for fragmented microplastic particles is calculated using the following formula: ; in, is the Aschenbrenner coefficient for fragmented microplastic particles, which represents the non-spherical morphological characteristics formed by the combination of the three principal axis dimensions of the fragmented microplastic particles, and takes a value greater than 0. The length of the major axis of the fragmented microplastic particles represents the largest principal axis dimension in the three-dimensional envelope structure, in mm. The short axis length of the fragmented microplastic particles represents the smallest principal axis dimension in the three-dimensional envelope structure, in mm; The length of the intermediate axis of the fragmented microplastic particles represents the principal axis dimension in the three-dimensional envelope structure located between the major and minor axis lengths, in mm.

[0118] The Aschenbrenner coefficient for fibrous microplastic particles is calculated using the following formula: ; in, is the Aschenbrenner coefficient for fibrous microplastic particles, which represents the non-spherical morphological characteristics formed between the axial length and cross-sectional diameter of the fibrous microplastic particles, and takes a value greater than 0. The diameter of the fibrous microplastic particles represents the characteristic dimension of the fiber cross-section, in mm. The length of the fibrous microplastic particles represents the axial extension dimension of the fibers, in mm.

[0119] The Corey coefficient for fragmented microplastic particles is calculated using the following formula: ; in, The Corey coefficient is the ratio of the short axis length of the fragmented microplastic particles to the combined scale of the long axis length and the intermediate axis length. It takes a value greater than 0 and not greater than 1. , and The definition is consistent with the one mentioned above.

[0120] The Corey coefficient for fibrous microplastic particles is calculated using the following formula: ; in, The Corey coefficient is the ratio of the cross-sectional diameter of the fiber to the combined diameter and axial length of the fiber, and its value is greater than 0 and not greater than 1. and The definition is consistent with the one mentioned above.

[0121] The formula for calculating the Janke coefficient of fragmented microplastic particles is as follows: ; in, Janke coefficient is the ratio of the short axis length of the fragmented microplastic particles to the root mean square scale of the three principal axes. It takes a value greater than 0 and not greater than 1. , and The definition is consistent with the one mentioned above.

[0122] The formula for calculating the thin length of fragmented microplastic particles is as follows: ; in, The length of the fragmented microplastic particles is the ratio between the length of the intermediate axis and the length of the major axis of the fragmented microplastic particles. The value is greater than 0 and not greater than 1. and The definition is consistent with the one mentioned above.

[0123] The formula for calculating the thin length of fibrous microplastic particles is as follows: ; in, The fine length of the fibrous microplastic particles represents the ratio between the cross-sectional diameter and the axial length of the fiber, and its value is greater than 0 and not greater than 1. and The definition is consistent with the one mentioned above.

[0124] The formula for calculating the flatness of fragmented microplastic particles is as follows: ; in, The flatness of the fragmented microplastic particles represents the ratio between the short axis length and the intermediate axis length of the fragmented microplastic particles, and its value is greater than 0 and not greater than 1. and The definition is consistent with the one mentioned above.

[0125] The formula for calculating the flatness of fibrous microplastic particles is as follows: ; in, The flatness of the fibrous microplastic particles represents the ratio between the two orthogonal diameter directions of the fiber cross-section; The definition is consistent with the one mentioned above.

[0126] The formula for calculating the sphericity of fragmented microplastic particles is as follows: ; in, The sphericity of the fragmented microplastic particles represents the degree to which the actual surface morphology of the fragmented microplastic particles closely resembles the surface morphology of a sphere of the same volume. The value is greater than 0 and not greater than 1. The surface area of ​​a sphere with the same volume as the fragmented microplastic particles is represented by the surface dimension of a sphere of the same volume, in mm. 2 ; This represents the actual surface area of ​​the fragmented microplastic particles, indicating the surface size of the particles in contact with the surrounding fluid, expressed in mm. 2 ; The equivalent diameter is determined based on the volume of the fragmented microplastic particles, representing the diameter of a sphere with the same volume as the fragmented microplastic particles, in mm. The equivalent area diameter is determined based on the projected area of ​​the fragmented microplastic particles. It represents the diameter of a circle with the same projected area as the fragmented microplastic particles, and is expressed in mm.

[0127] The formula for calculating the sphericity of fibrous microplastic particles is as follows: ; in, The sphericity of the fibrous microplastic particles represents the degree to which the actual surface morphology of the fibrous microplastic particles closely resembles the surface morphology of a sphere of the same volume. The value is greater than 0 and not greater than 1. The surface area of ​​a sphere with the same volume as the fibrous microplastic particles, in mm. 2 ; This refers to the actual surface area of ​​the fibrous microplastic particles, in mm². 2 ; and The definition is consistent with the one mentioned above.

[0128] The formula for calculating the roundness of fragmented microplastic particles is as follows: ; in, The circularity of the fragmented microplastic particles represents the degree of deviation of the two-dimensional projected boundary of the fragmented microplastic particles from the boundary of a circle with equal area, and the value is greater than 0. The perimeter of the two-dimensional projected outline of the fragmented microplastic particles represents the length of the actual projected boundary, in mm. The circumference of a circle with the same projected area as the fragmented microplastic particles is represented by the boundary length of the circle with the same area, in mm. This is the corrected roundness factor for fragmented microplastic particles. It represents the correction ratio of the two-dimensional projected shape of the fragmented microplastic particles relative to the circular projected shape, and its value is greater than 0.

[0129] The formula for calculating the sphericity of fibrous microplastic particles is as follows: ; in, The circularity of the fibrous microplastic particles represents the degree of deviation of the two-dimensional projected boundary of the fibrous microplastic particles from the boundary of a circle of equal area, and the value is greater than 0. The perimeter of the two-dimensional projected outline of the fibrous microplastic particles is shown in mm. The circumference of a circle with the same projected area as the fibrous microplastic particles, in mm; Pi; and The definition is consistent with the one mentioned above.

[0130] The formula for calculating the Delino coefficient of fragmented microplastic particles is as follows: ; in, is the Delino coefficient for fragmented microplastic particles, which represents the comprehensive morphological characteristics determined by the sphericity and roundness of fragmented microplastic particles, and takes a value greater than 0; , , , and The definition is consistent with the one mentioned above.

[0131] The formula for calculating the Delino coefficient of fibrous microplastic particles is as follows: ; in, is the Delino coefficient of fibrous microplastic particles, which represents the comprehensive morphological characteristics determined by the sphericity and roundness of fibrous microplastic particles, and takes a value greater than 0; , , , and The definition is consistent with the one mentioned above.

[0132] The formula for calculating the aspect ratio of fragmented microplastic particles is as follows: ; in, The aspect ratio of the fragmented microplastic particles represents the ratio between the largest and smallest principal axis dimensions of the fragmented microplastic particles, and its value is not less than 1. and The definition is consistent with the one mentioned above.

[0133] The formula for calculating the aspect ratio of fibrous microplastic particles is as follows: ; in, The aspect ratio of fibrous microplastic particles represents the ratio between the axial length of the fiber and the diameter of the cross-section, and its value is not less than 1. and The definition is consistent with the one mentioned above.

[0134] For each microplastic particle, the calculated morphological characterization parameters are correlated with particle identification, particle morphology category, particle density, and stable settling velocity to form the input data for the drag force model. Fragmented microplastic particles use a fragment morphological parameter set, fibrous microplastic particles use a fiber morphological parameter set, and real microplastic samples use the corresponding morphological parameter set according to their morphological category. The morphological parameter set for fragmented microplastic particles is denoted as... It contains , , , , , , , and At least one of the following; the set of morphological parameters of fibrous microplastic particles is denoted as... It contains , , , , , , and At least one of them.

[0135] See attached document Figure 4 Step S200 involves constructing a complex-shaped microplastic drag force model and calibrating it with real samples. Step S200 is executed through the morphology parameter construction module and includes the following sub-steps.

[0136] Sub-step S201 establishes the correspondence between particle Reynolds number, morphological characterization parameters, and sedimentation results. Read the stable settling velocity, particle density, particle geometry, and morphological characteristics of 100 typical microplastic particles. Match the data according to the particle identifier and delete records with inconsistent particle identifiers, missing data fields, or those that have not reached a stable settling state.

[0137] The particle Reynolds number was determined based on the steady-state settling velocity of the particles, fluid density, hydrodynamic viscosity, and particle characteristic size. The characteristic size of fragmented microplastic particles was determined using the equivalent diameter, while the characteristic size of fibrous microplastic particles was determined using the characteristic size corresponding to the dragging direction. The selection rules for particle characteristic size remained consistent across the same model building batch.

[0138] The particle Reynolds number, morphological parameters, and steady-state settling velocity were recorded in the same sample record. The sample records were grouped according to particle morphology, allowing fragmented microplastic particle samples and fibrous microplastic particle samples to participate in model fitting separately.

[0139] Each model construction sample includes at least particle identifier, particle morphology category, particle density, particle characteristic size, stable settling velocity, particle Reynolds number, and corresponding morphological characterization parameters. The sample data is arranged in a uniform data field order before being written into the nonlinear regression program.

[0140] Sub-step S202 uses nonlinear regression to determine the drag force function relationship of complex-shaped microplastics. Based on the particle-fluid interaction, the drag coefficient is defined as a function of the particle Reynolds number and morphological parameters. The drag force function relationship is as follows: ; in, This is the particle morphology category index, and its value is... or , representing fragmented microplastic particles and fibrous microplastic particles, respectively; For category The corresponding drag coefficient represents the intensity of the dragging effect of the fluid relative to this type of microplastic particles, and its value is greater than 0. For category The corresponding particle Reynolds number represents the ratio of inertial action to viscous action in the relative motion of particles and fluid of this type, and its value is not less than 0; For category The corresponding set of morphological representation parameters represents the model input consisting of at least one of the following categories: Aschenbrenner coefficient, Corey coefficient, Janke coefficient, slenderness, flatness, sphericity, roundness, Delino coefficient, and aspect ratio. For category The corresponding drag force fitting function operation notation represents the mapping relationship between the particle Reynolds number and morphological characterization parameters determined by nonlinear regression and the drag force coefficient. This operation notation is stored as a function object in the calculation program, not as a flatness scalar field.

[0141] The Levenburg-Marquardt algorithm was used to perform nonlinear regression. The regression calculation used the residual between the model-predicted steady-state settlement velocity and the experimental steady-state settlement velocity as the target data, and the sum of squared residuals was reduced by successively adjusting the regression parameters. In each iteration, the prediction results and residuals of all model-built samples were recalculated.

[0142] Regression stopping conditions include the relative increment of parameters not exceeding the parameter convergence threshold, the relative change of the objective function not exceeding the target convergence threshold, or the number of iterations reaching the iteration limit. The parameter convergence threshold, target convergence threshold, and iteration limit are written to the model configuration file before model fitting begins and remain unchanged throughout the same fitting task.

[0143] A fragment drag force model was established for fragmented microplastic particles, and a fiber drag force model was established for fibrous microplastic particles. The model output data includes regression parameters, objective function values, sample residuals, applicable particle types, and parameter convergence status.

[0144] Sub-step S203: Verify and calibrate the drag force model parameters using real microplastic samples. Three-dimensional morphological data and stable settling velocities of 50 real microplastic samples were collected. Corresponding morphological characterization parameters were calculated based on the morphological categories of the real microplastic samples, and these parameters, along with the particle Reynolds number, were input into the corresponding drag force model.

[0145] The predicted steady-state settling velocity of real microplastic samples was calculated using a drag force model, and the predicted steady-state settling velocities were correlated one-to-one with the experimental steady-state settling velocities. The mean absolute error, coefficient of determination, and root mean square error were calculated respectively.

[0146] The evaluation results of the drag force model of this invention were compared with the evaluation results of existing debris drag force models and existing fiber drag force models. All models used the same real microplastic samples, the same stable settling velocity data, and the same error calculation rules.

[0147] When the evaluation results do not meet the preset model evaluation threshold, real microplastic samples with errors exceeding the single-sample error limit are added to the calibration dataset, and nonlinear regression is re-executed. The preset model evaluation threshold and single-sample error limit are written into the validation configuration file before model validation begins and remain unchanged until model validation is completed.

[0148] After re-executing the nonlinear regression, the predicted stable settling velocity and evaluation indices were recalculated using the same 50 sets of real microplastic samples. Once the preset model evaluation threshold was reached, the drag force model parameters and the applicable particle types were saved, and the drag force model parameters were sent to the fluid-structure interaction calculation module.

[0149] See attached document Figure 5 Step S300: Establish a fluid-structure interaction numerical framework that considers complex particle morphology and interphase back diffusion. Step S300 is executed through the fluid-structure interaction calculation module and includes the following sub-steps.

[0150] Sub-step S301: Establish the turbid fluid domain and particle domain and set initial and boundary conditions.

[0151] A three-dimensional computational domain is established based on the geometry of the sedimentation column or flume experiment, and the fluid domain is discretized using an Eulerian grid. The grid data includes grid node coordinates, grid cell volume, grid adjacency relationships, and boundary grid identifiers.

[0152] The experimental setup includes a turbidity inlet, a fluid outlet, a top boundary, sidewall boundaries, and a bed boundary. Fluid velocity, concentration, and turbulence parameters are set at the turbidity inlet. Pressure conditions are set at the fluid outlet. Velocity constraints and particle contact conditions are set at the sidewall and bed boundaries.

[0153] Sediment particles and microplastic particles are established within the particle domain. For each particle, a particle identifier, initial position, initial translational velocity, initial angular velocity, initial attitude, particle density, particle size, particle morphology category, and contact properties are set.

[0154] The computational domain size, inlet conditions, particle placement location, particle quantity, bed structure, and measurement locations in the validation test were kept consistent with those in the corresponding flume model experiment. Separate test labels were established for each validation test to prevent the mixing of input and output data from different tests.

[0155] Fluid initial conditions, fluid boundary conditions, particle initial conditions, and particle contact properties are written into the input file for the corresponding operating condition. After reading the operating condition identifier, the fluid-structure interaction calculation module only calls the computational domain data and parameter data associated with that operating condition identifier.

[0156] Sub-step S302 uses a finite volume discretization and pressure-velocity coupled algorithm to solve for the turbid fluid phase. Within each fluid time step, the fluid velocity field, pressure field, concentration field, turbulence parameter field, particle volume fraction field, and particle momentum source term of the previous time step are first read. For the first fluid time step, the initial fluid conditions and initial particle volume fraction field are read.

[0157] The fluid phase control equations are spatially discretized using the finite volume method, and mass flux and momentum flux are calculated based on the grid cells. A phase-coupled semi-implicit pressure correlation equation algorithm is then used to sequentially solve for the volume fraction, velocity prediction, pressure correction, and velocity correction.

[0158] The turbulent parameter field is updated using a renormalized group k-ω turbulence model, and the updated turbulence parameters are used for fluid momentum transport calculations. The convergence condition for fluid phase iteration is jointly determined by the continuity residual, velocity residual, and pressure residual, and the threshold values ​​for each residual are written into the solution configuration file before the calculation begins.

[0159] When all fluid phase residuals are not greater than their corresponding residual thresholds, the velocity field, pressure field, concentration field, and turbulence parameter field of the current fluid time step are output. When any residual exceeds its corresponding residual threshold, pressure and velocity correction calculations continue until the convergence condition is met or the fluid phase iteration upper limit is reached.

[0160] If the convergence condition is not met after reaching the upper limit of fluid phase iteration, record the non-converged time step, the corresponding mesh region, and the residual type, and stop the current calculation. After checking the mesh quality, time step size, and boundary conditions, re-execute the current calculation.

[0161] Sub-step S303 performs particle volume fraction diffusion mapping and fluid momentum reverse diffusion processing. See attached document Figure 6 The fluid phase solution process sequentially executes the following steps: reading initial fluid conditions, reading particle volume fraction, solving the velocity field, solving for pressure corrections, updating the pressure field, and updating the velocity field. The particle phase solution process sequentially executes the following steps: reading initial particle conditions, calculating particle contact forces, calculating particle surface interactions, calculating particle volume interactions, updating particle momentum, and updating particle state.

[0162] At the coupling time point, the fluid and particle phases exchange particle volume fraction, particle momentum source term, fluid velocity, fluid pressure, and fluid turbulence parameters. After the fluid phase solution is completed, the meshed fluid data is interpolated to the particle locations. After the particle phase solution is completed, the particle-occupied volume and particle momentum source term are mapped to the fluid mesh.

[0163] See attached document Figure 7 First, the fluid grid cell containing the center of each particle is determined, and the volume occupied by the particle is written into the corresponding fluid grid cell. Then, according to the grid adjacency relationship and spatial distance, the volume occupied by the particle is diffused to the adjacent fluid grid cells.

[0164] The volume diffusion process maintains the total volume of each individual particle before and after mapping, and also maintains the total volume of all particles before and after mapping. The particle volume fraction is determined by the volume occupied by the particles in each fluid mesh cell and the volume of the fluid mesh cell.

[0165] During the momentum exchange phase, fluid reverse diffusion is performed on the particle momentum source term according to the spatial weights used in the volume diffusion process. The fluid reverse diffusion process distributes the particle momentum influence to the grid where the particle is located and adjacent grids, while keeping the total momentum exchange between the particle phase and the fluid phase constant.

[0166] The neighborhood range and spatial weights used for volumetric diffusion are determined before the start of the current computational case and remain unchanged within a single computational case. Momentum anti-diffusion uses the neighborhood relations corresponding to volumetric diffusion, enabling the particle volume fraction mapping process and momentum exchange process to use corresponding spatial data.

[0167] See attached document Figure 8 Step S400 calculates the particle-fluid interaction, particle-contact interaction, and microplastic transport and deposition process. Step S400 is executed through the transport and deposition analysis module and includes the following sub-steps.

[0168] Sub-step S401: Calculate the interaction between particles and turbidity flow and determine the particle vortex interaction time. Within each particle time step, fluid velocity, fluid pressure, fluid density, fluid concentration, and turbulence parameters are interpolated from the fluid grid to the particle location.

[0169] The drag force, lift force, pressure gradient force, and virtual mass force acting on the particles were calculated separately. The drag force of the microplastic particles was calculated using the complex-morphology microplastic drag force model constructed in step S200. The drag force of the sediment particles was calculated according to their corresponding particle parameters and drag force relationships.

[0170] The dispersion effect of turbulent flow is characterized by the particle-vortex interaction time. The formula for calculating the particle-vortex interaction time is as follows: ; in, is the particle-vortex interaction time, which represents the effective time for a microplastic particle to be continuously subjected to the same turbulent vortex, in seconds, and has a value greater than 0. The vortex duration period represents the duration of a turbulent vortex from its formation to its failure, measured in seconds, and is greater than 0. is the particle transport time, which represents the time required for a microplastic particle to pass through the scale of the considered vortex effect, in seconds, and has a value greater than 0. This is the minimum value operator, which selects the smaller value between the vortex duration period and the particle transport time.

[0171] The current vortex parameters are maintained on the particles during the particle-vortex interaction time. When the particle-vortex interaction time ends, the turbulence parameters at the particle's location are reread, and the vortex interaction state is updated. This process is synchronized with the fluid time step and the particle time step.

[0172] The particle-fluid interaction calculation results are stored according to particle identification, including drag effect results, rise effect results, pressure gradient effect results, virtual mass effect results, and the current particle-vortex interaction time. The calculation results serve as input for updating the particle motion state.

[0173] Sub-step S402: Calculate particle contact response and flexible deformation of complex-shaped microplastic nodes. The contact relationships between sediment particles, between sediment particles and microplastic particles, between microplastic particles, and between particles and the substrate were examined. For each contact pair, the contact normal direction, normal overlap, tangential relative displacement, and contact duration were determined.

[0174] The normal elastic and normal damping effects were calculated using the Hertz spring-damping model. The tangential contact effect was calculated using the Mindlin-Deresiewicz tangential contact model, and the tangential contact effect was limited based on the particle friction parameters.

[0175] For fibrous microplastic particles, multiple spherical cylindrical units are connected sequentially along the particle axis. For fragmented and film-like microplastic particles, multiple rounded triangular prism units are connected according to the three-dimensional surface structure of the particles. The number of connecting units is determined by the upper limit of the three-dimensional morphological discretization error.

[0176] The upper limit of the three-dimensional morphological discretization error is determined before the particle node model is established. The number of connecting units is gradually increased, and the increase in the number of connecting units is stopped when the rate of change of the total particle volume, the rate of change of the particle outer surface area, and the rate of change of the principal axis size before and after increasing the number of connecting units are all no greater than the upper limit of the three-dimensional morphological discretization error.

[0177] At each connection node, the nodal linear elasticity, nodal bending moment, and nodal torsional moment are calculated, and the nodal damping is calculated based on the relative velocity of the nodes. The position and orientation of each connection element are updated based on the resultant force and resultant moment of the nodes to obtain the flexible deformation state of the microplastic particles under the action of turbulent flow and particle collision.

[0178] The particle node model is established while maintaining consistency with the 3D morphological data in terms of total particle volume, particle mass, and principal axis dimensions. The mass of each connecting unit is allocated according to the proportion of its volume in the total particle volume, and the initial orientation of each connecting unit is determined based on the 3D surface structure of the particle.

[0179] Sub-step S403: Perform bidirectional coupling iteration of fluid particles and identify the deposition and burial state. The fluid, contact, gravitational, and nodal effects on the particle are combined, and the particle's translational velocity, angular velocity, spatial position, and attitude are updated. After updating the particle's state, the particle's occupied volume and momentum source term are recalculated.

[0180] The updated particle volume fraction and particle momentum source term are sent to the fluid phase solver, which recalculates the velocity, pressure, concentration, and turbulence parameter fields. The fluid phase calculation results are then interpolated back to the particle locations, forming a two-way coupled iteration.

[0181] The current coupling time step is completed when the fluid residual, particle velocity change rate, and particle momentum exchange change rate at the current coupling time step are all no greater than their respective convergence thresholds. Each convergence threshold is written to the coupling configuration file before the calculation begins and remains unchanged in a single calculation case.

[0182] Particle state is identified based on vertical position, particle velocity, and duration of contact with the substrate. Particles not in contact with the substrate but in motion are marked as suspended or near-bed transported. Particles in continuous contact with the substrate and with a velocity not exceeding the deposition rate threshold are marked as deposited. Particles covered by sediment particles with a thickness reaching the particle burial depth are marked as buried.

[0183] The deposition rate threshold is determined based on the ratio of particle location measurement resolution to particle time step. The particle burial depth is determined based on the minor axis dimension or cross-sectional diameter of the target particle, and a consistent determination rule is applied within the same particle category.

[0184] The start and end times of each state were recorded for particles in suspension, near-bed transport, sedimentation, and burial states. The statistical unit calculated the particle suspension duration, near-bed transport duration, sedimentation location, and burial depth based on the particle state records.

[0185] See attached document Figure 9 Step S500 involves performing settlement benchmark, flume condition verification, and sensitivity analysis of main control parameters. Step S500 is executed through the model verification and evaluation module and includes the following sub-steps.

[0186] Sub-step S501: Establish a numerical benchmark consistent with the static water settling experiment and verify the settling results. A static water computational domain was established based on the geometry of the sedimentation column, and fluid density, fluid viscosity, particle release location, and observation area were set consistent with those of the sedimentation experiment.

[0187] Read the three-dimensional morphology, particle density, particle size, and drag force model parameters of the corresponding microplastic particles. Set the particle attitude according to the initial attitude of the sedimentation experiment, and perform particle sedimentation calculations in a static fluid.

[0188] Extract the simulated sedimentation curves and simulated steady-state sedimentation velocities after the particles enter the observation area. Align the simulated sedimentation curves with the experimental sedimentation curves according to the sedimentation time, and match the simulated steady-state sedimentation velocities with the experimental steady-state sedimentation velocities according to the particle identification.

[0189] Calculate the mean absolute error, coefficient of determination, and root mean square error for all reference samples. If the evaluation results meet the preset settlement verification threshold, save the current drag force model parameters. If the evaluation results do not meet the preset settlement verification threshold, send particle data with errors exceeding the single sample error limit to step S200 for recalibration.

[0190] The computational domain, initial particle orientation, fluid properties, and observation location used in the sedimentation benchmark verification process are correlated one-to-one with the corresponding sedimentation experiments. The model validation and evaluation module saves the simulated sedimentation curve, experimental sedimentation curve, and error evaluation results for each particle.

[0191] Sub-step S502: Establish five typical numerical flume operating conditions and compare velocity concentration and spatial distribution. A numerical flume was established based on the geometric conditions, inlet conditions, particle feeding conditions, substrate conditions, and measurement locations of the flume model experiment. Five typical experimental conditions were selected, and each experimental condition was assigned a condition label and an independent input file.

[0192] For each typical experimental condition, steps S300 and S400 were performed to obtain the turbidity flow velocity field, turbidity concentration field, sediment particle distribution, and microplastic particle distribution. Velocity and concentration profiles were extracted according to the experimental measurement locations.

[0193] The simulated and measured flow velocity profiles were aligned using the same vertical coordinate system, as were the simulated and measured concentration profiles. The number of simulated and measured microplastic particles was then counted according to the spatial division of the water tank.

[0194] Calculate the velocity profile error, concentration profile error, and microplastic spatial distribution error separately. If all five typical experimental conditions meet their corresponding validation thresholds, the fluid-structure interaction numerical model is considered validated under the water tank condition. If any typical experimental condition fails to meet the validation threshold, record the corresponding time, measurement location, and output variables, and perform parameter calibration.

[0195] Parameter calibration is performed according to the data type corresponding to the error. When the velocity profile error exceeds the corresponding verification threshold, check the fluid inlet conditions, turbulence parameters, mesh settings, and pressure-velocity coupling settings. When the concentration profile error exceeds the corresponding verification threshold, check the initial turbidity concentration conditions, particle volume fraction mapping settings, and momentum back-diffusion settings. When the spatial distribution error of microplastic particles exceeds the corresponding verification threshold, check the drag force model parameters, particle contact properties, and particle node model settings.

[0196] Sub-step S503: Change the initial settings of the main control factors and analyze the particle collision force chain and deposition response. The following parameters were selected for sensitivity analysis: turbidity inlet velocity, initial turbidity concentration, sediment particle concentration, microplastic particle density, microplastic particle size, microplastic particle morphology, particle friction properties, and particle node discreteness.

[0197] Each sensitivity calculation changes only one target parameter, while all other input conditions remain unchanged. The target parameter takes values ​​according to a preset parameter sequence, and each value establishes an independent operating condition identifier. The preset parameter sequence is written to the parameter configuration file before the sensitivity calculation begins.

[0198] The same calculation time and output rules are applied to all variable parameter conditions. The transport distance, lateral diffusion range, vertical diffusion range, suspension duration, deposition location, burial depth, number of collisions, number of frictions, and force chain distribution between particles of microplastics are statistically analyzed.

[0199] The results of each variable parameter condition were compared with the baseline condition to determine the transport and deposition response corresponding to the change in target parameters. The collision and friction processes between microplastic particles and sediment particles were analyzed by considering the number, direction, and duration of interparticle force chains, and the impact of particle interactions on the final deposition location and burial distribution was determined.

[0200] The results of parameter sensitivity analysis are stored in association with the target parameter name, target parameter value, operating condition identifier, and outcome variable. The model validation and evaluation module generates transport and deposition response data corresponding to different main control factors based on the changes of each outcome variable relative to the baseline operating condition results.

[0201] Specific application examples: See attached document Figure 10 In this embodiment, microplastic samples obtained from a nearshore area and experimental data from a matching water tank are used to simulate the transport and deposition of microplastics in turbidity currents.

[0202] Appendix Figure 10 The x-axis is set to time, named "Time," with units in seconds (s). The x-axis range is from 0s to 8s, and the main scale is set in 1-second intervals. (See attached image.) Figure 10 Settlement distance is used as the ordinate, named "Settlement Distance," and the unit is cm. The ordinate display range is from 0cm to 35cm, with major scales set at 5cm intervals. A background grid of intersecting dashed lines is set along the time and settlement distance directions within the plotting area to correspond to each time scale and settlement distance scale.

[0203] Appendix Figure 10 This includes sedimentation curves for examples of fragmented microplastics, fibrous microplastics, and real samples. All three sedimentation curves are drawn in black and distinguished by their line type and data marker shapes. The sedimentation curve for fragmented microplastics is represented by a solid black line and a black circle; the sedimentation curve for fibrous microplastics is represented by a dashed black line and a black square; and the sedimentation curve for the real sample is represented by a dotted-dash line and a black triangle. Corresponding legends are located in the upper left corner of the plotting area, indicating the examples of fragmented microplastics, fibrous microplastics, and real samples, respectively.

[0204] Appendix Figure 10 All three curves start at time 0s and a settling distance close to 0cm, and extend continuously in the direction of increasing settling distance as time increases. The settling curve for the fragmented microplastic example is located at the upper part of the three curves, the settling curve for the fibrous microplastic example is located in the middle part of the three curves, and the settling curve for the real sample example is located at the lower part of the three curves. Under the same time conditions, the cumulative settling distance corresponding to the fragmented microplastic example is greater than that corresponding to the fibrous microplastic example, and the cumulative settling distance corresponding to the fibrous microplastic example is greater than that corresponding to the real sample example.

[0205] Appendix Figure 10 The curves in the data show a transition from a low slope to a stable slope in the initial time period, followed by a continuously increasing settling distance in subsequent time periods. At approximately 2 seconds, the settling distance for the fragmented microplastic example was approximately 6.3 cm, for the fibrous microplastic example approximately 3.4 cm, and for the real sample example approximately 1.7 cm. At approximately 4 seconds, the settling distance for the fragmented microplastic example was approximately 15.1 cm, for the fibrous microplastic example approximately 10.1 cm, and for the real sample example approximately 5.6 cm. At approximately 6 seconds, the settling distance for the fragmented microplastic example was approximately 24.8 cm, for the fibrous microplastic example approximately 18.2 cm, and for the real sample example approximately 10.9 cm. At 8 seconds, the settling distance for the fragmented microplastic example was approximately 34.2 cm, for the fibrous microplastic example approximately 25.5 cm, and for the real sample example approximately 16.8 cm. The circular, square, and triangular markers on the curve correspond to the settlement distance data at each time sampling location.

[0206] This embodiment includes 150 sets of static water settling experiments, of which 100 sets of typical microplastic particle settling experiments are used to establish a drag force model, and 50 sets of real microplastic sample settling experiments are used for model verification and parameter calibration. A high-speed camera and lens are positioned 10 cm above the bottom of the settling column.

[0207] A fragmented microplastic particle was selected for morphological parameter calculation. The major axis length of this fragmented microplastic particle was calculated. The length of the intermediate shaft is 10mm. The minor axis length is 6mm. It is 2mm.

[0208] Substituting the above values ​​into the formula for calculating the Aschenbrenner coefficient of fragmented microplastic particles, we obtain... The calculation process involves multiplying 10 by 2 and then dividing by the square of 6, resulting in 0.5556. This result is associated with the particle identifier and written into the debris drag force model input data.

[0209] Substituting the above values ​​into the Corey coefficient calculation formula for fragmented microplastic particles, we obtain... The calculation process involves dividing 2 by the square root of the product of 10 and 6, yielding a result of 0.2582. This calculation indicates that the minor axis dimension of the fragmented microplastic particle is smaller than the combined scale formed by the major axis and the intermediate axis, thus the system retains the particle within the set of fragment morphology parameters.

[0210] Substituting the above values ​​into the formula for calculating the Janke coefficient of fragmented microplastic particles, we obtain... The calculation process is to divide 2 by the sum of 4, 36 and 100, and then divide by 3 to get the square root. The result is 0.2928.

[0211] Substituting the above values ​​into the formula for calculating the thinness of fragmented microplastic particles, we obtain... The calculated result is 0.6000. Substituting the above value into the formula for calculating the flatness of fragmented microplastic particles, we get... The calculated result is 0.3333. Substituting the above value into the formula for calculating the aspect ratio of fragmented microplastic particles, we get... The calculated result is 5.0000.

[0212] The surface area of ​​a sphere of the same volume of the fragmented microplastic particles It is 50.27mm. 2 actual surface area It is 78.54mm 2 equivalent diameter It is 4.00mm, with an equivalent area diameter of 4.00mm. It is 5.00mm.

[0213] Substituting the above values ​​into the formula for calculating the sphericity of fragmented microplastic particles, 50.27 divided by 78.54 yields 0.6400, and 4.00 divided by 5.00 squared also yields 0.6400. Therefore, the sphericity of this fragmented microplastic particle is... It is 0.6400.

[0214] The perimeter of the two-dimensional projected profile of the fragmented microplastic particles The circumference of a circle with a projected area of ​​30.00 mm. The value is 24.00 mm. Substituting this value into the formula for calculating the roundness of fragmented microplastic particles, we obtain the roundness. The value is 1.2500. This is based on the sphericity of the fragmented microplastic particles. With roundness The ratio is calculated to obtain the Delino coefficient. It is 0.5120.

[0215] The morphological parameter construction module calculates the Aschenbrenner coefficient of the fragmented microplastic particles. Corey coefficient Janke coefficient slender length Flatness sphericity Circularity Delino coefficient and length-to-diameter ratio The particle was correlated with the experimental stable settling velocity and assigned to the debris drag force model.

[0216] A single fibrous microplastic particle was selected for morphological parameter calculation. The diameter of this fibrous microplastic particle was... It is 1.00mm in length. It is 8.00mm.

[0217] Substituting the above values ​​into the formula for calculating the Aschenbrenner coefficient of fibrous microplastic particles, we obtain... The calculated result is 8.0000. Substituting the above value into the Corey coefficient calculation formula for fibrous microplastic particles, we obtain... The calculated result is 0.3536.

[0218] Substituting the above values ​​into the formula for calculating the thinness of fibrous microplastic particles, we obtain... The calculated result is 0.1250. Substituting the above value into the formula for calculating the flatness of fibrous microplastic particles, we obtain... The calculated result is 1.0000. Substituting the above value into the formula for calculating the aspect ratio of fibrous microplastic particles, we get... The calculation result is 8.0000.

[0219] diameter For 1.00mm and length Substituting 8.00 mm into the formula for calculating the sphericity of fibrous microplastic particles, we obtain the sphericity. The value is 0.6353. Substituting the same value into the formula for calculating the roundness of fibrous microplastic particles, we obtain the roundness. It is 1.7952. Based on the sphericity of the fibrous microplastic particles... With roundness The ratio is calculated to obtain the Delino coefficient. It is 0.3539.

[0220] The morphological parameter construction module correlates the morphological characterization parameters of the fibrous microplastic particle with the experimental stable settling velocity and assigns the particle to the fiber drag force model.

[0221] During the construction of the drag force model, 100 sets of typical microplastic particle data were input into the Levonburg-Marquardt algorithm. After the model fitting was completed, 50 sets of real microplastic samples were input into the corresponding drag force model one by one, and the predicted steady-state settling velocity was output. The predicted steady-state settling velocity was compared with the experimental steady-state settling velocity according to particle identification.

[0222] In the water tank simulation, the fluid phase was discretized using the finite volume method, and the pressure and velocity fields were solved using a phase-coupled semi-implicit pressure correlation equation algorithm. The turbulent flow process was calculated using a renormalized group k-ω turbulence model. The normal contact response of particles was modeled using the Hertzian spring-damped model, and the tangential contact response was modeled using the Mindlin-Deresiewicz tangential contact model.

[0223] In this embodiment, the fibrous microplastic particles are constructed using eight spherical cylindrical elements, while the fragmented microplastic particles are constructed using six rounded triangular prism elements. The forces, moments, and deformations at the connection nodes are calculated using a nodal linear elastic model and nodal damping.

[0224] Within one coupling time step, the vortex duration period The particle transport time is 0.12s. The value is 0.08 s. Substituting this value into the formula for calculating the particle-vortex interaction time, and taking the smaller value between 0.12 s and 0.08 s, we obtain the particle-vortex interaction time. It takes 0.08 seconds.

[0225] The transport and deposition analysis module uses 0.08 s as the effective time for the current turbulent vortex to continuously act on the microplastic particle. After 0.08 s, the system rereads the turbulence parameters at the particle's location and updates the turbulent dispersion effect on the particle.

[0226] Figure 10 The sedimentation curves of microplastic particles of different morphologies were plotted using the same time and sedimentation distance coordinates. The video processing unit extracted the stable sedimentation velocity based on the intervals where the curve slope was continuous and stable, and correlated the stable sedimentation velocity with the corresponding particle morphology characterization parameters.

[0227] The data markers in the sedimentation curves for fragmented microplastics, fibrous microplastics, and real samples are associated with the corresponding particle identifiers and video frame times, respectively. The video processing unit calculates segmented sedimentation velocities using the time difference and sedimentation distance difference between adjacent data markers, and determines stable sedimentation intervals by using the portions of the curves where multiple consecutive segmented sedimentation velocities remain stable. The line shapes and marker shapes of the three curves are only used to distinguish different particle types and do not change the calculated sedimentation distance and sedimentation time results.

[0228] Experimental verification and effect comparison: See attached document Figure 11 In this embodiment, model verification is performed in the order of settlement benchmark verification, numerical flume verification, and parameter sensitivity analysis.

[0229] Appendix Figure 11 The x-axis is set to normalized flow rate or concentration, named "Normalized Flow Rate or Concentration," and ranges from 0.0 to 1.0, with major scale increments of 0.2. (See attached image.) Figure 11 The normalized height is used as the ordinate, named "Normalized Height," and ranges from 0.0 to 1.0, with major scale increments of 0.2. A dashed background grid is set along the normalized flow velocity or concentration direction and the normalized height direction within the plotting area, ensuring that the positions of each measured data point and simulated curve correspond to their respective normalized coordinates.

[0230] Appendix Figure 11 This includes a normalized flow velocity profile (based on measured data), a normalized flow velocity profile (based on simulated data), a normalized concentration profile (based on measured data), and a normalized concentration profile (based on simulated data). All four profile curves are drawn in black and distinguished by data markers and line types. The normalized flow velocity profile is represented by a solid black line and a black circle; the normalized flow velocity profile is represented by a dashed black line without data markers; the normalized concentration profile is represented by a dotted line and a black square; and the normalized concentration profile is represented by a dashed black line and a hollow triangle. Corresponding legends are located in the upper right corner of the plotting area, indicating the normalized flow velocity profile, the normalized flow velocity profile, the normalized concentration profile, and the normalized concentration profile, respectively.

[0231] Appendix Figure 11The normalized velocity profile is composed of multiple black circular measured data markers and solid black lines connecting the data markers. The normalized velocity at a normalization height of 0.0 is approximately 0.32. As the normalization height increases, it first extends in the direction of increasing normalized velocity, reaching approximately 0.56 at a normalization height of 0.1, approximately 0.81 at a normalization height of 0.2, and reaching a normalized velocity close to 1.0 at a normalization height of 0.3. It also maintains a normalized velocity close to 1.0 at a normalization height of approximately 0.4. Subsequently, the measured normalized velocity profile extends in the direction of decreasing normalized velocity as the normalized height continues to increase. The normalized velocity at a normalized height of 0.5 is approximately 0.81, at 0.6 it is approximately 0.56, at 0.7 it is approximately 0.32, at 0.8 it is approximately 0.16, at 0.9 it is approximately 0.05, and at 1.0 it is close to 0.

[0232] Appendix Figure 11 The simulated normalized velocity profile is represented by a continuous black dashed line without data markers. The simulated normalized velocity profile uses the same normalized height coordinates as the measured normalized velocity profile, and forms a profile profile corresponding to the measured normalized velocity profile as the normalized height increases from 0.0 to 1.0. In the lower and middle regions, the simulated normalized velocity profile extends towards the direction of higher normalized velocity, while in the upper region, it continuously contracts towards the direction of near-zero normalized velocity as the normalized height increases.

[0233] Appendix Figure 11 The normalized concentration profile consists of multiple black square measured data markers and black dashed lines connecting the data markers. The normalized concentration profile measured at a normalized height of 0.0 is 1.0, at 0.1 it is approximately 0.76, at 0.2 it is approximately 0.59, at 0.3 it is approximately 0.45, at 0.4 it is approximately 0.35, at 0.5 it is approximately 0.27, at 0.6 it is approximately 0.20, at 0.7 it is approximately 0.16, at 0.8 it is approximately 0.12, at 0.9 it is approximately 0.09, and at 1.0 it is approximately 0.07. The normalized concentration profile continuously extends in the direction of decreasing normalized concentration as the normalization height increases.

[0234] Appendix Figure 11The simulated normalized concentration profile consists of multiple hollow triangle markers and black dashed lines connecting them. The normalized concentration at a normalization height of 0.0 is 1.0, and it continuously decreases with increasing normalization height, forming a decay profile extending from the lower right to the upper left within the plotting area. Each hollow triangle marker corresponds to simulated concentration data at a different normalization height. The simulated normalized concentration profile is compared with the measured normalized concentration profile at the same normalization height to determine the deviation between the simulated and measured concentrations.

[0235] Appendix Figure 11 The measured normalized velocity profile and the simulated normalized velocity profile are used to compare the change of turbidity velocity along the normalized height direction, while the measured normalized concentration profile and the simulated normalized concentration profile are used to compare the change of turbidity concentration along the normalized height direction. Black circles and black squares represent measured data at corresponding measurement locations, while hollow triangles represent simulated concentration data at corresponding normalized height locations. Solid black lines and dashed black lines represent the data connection relationships between the measured normalized velocity profile and the measured normalized concentration profile, respectively. Black dashed lines without data markers represent the simulated normalized velocity profile, and black dashed lines with hollow triangles represent the simulated normalized concentration profile.

[0236] Settlement benchmark validation used 50 sets of real microplastic samples. The model evaluation thresholds were set to mean absolute error no greater than 1.00 mm / s, coefficient of determination no less than 0.90, and root mean square error no greater than 1.20 mm / s.

[0237] Fifty sets of real microplastic samples were input into the drag force model of this invention. The calculated mean absolute error was 0.42 mm / s, the coefficient of determination was 0.93, and the root mean square error was 0.56 mm / s. The above evaluation results meet the model evaluation threshold. The model verification and evaluation module saves the current drag force model parameters and uses the current parameters for subsequent tank working condition calculations.

[0238] Using a comparative model based solely on spherical particle relationships, calculations were performed on 50 identical real microplastic samples. The mean absolute error was 1.36 mm / s, the coefficient of determination was 0.74, and the root mean square error was 1.68 mm / s. Under the same samples and evaluation rules, the mean absolute error and root mean square error of the drag force model of this invention are lower than those of the comparative model based solely on spherical particle relationships, while the coefficient of determination is higher.

[0239] Five typical experimental conditions were set up for numerical flume validation. For each condition, simulated flow velocity profile, measured flow velocity profile, simulated concentration profile, measured concentration profile, and spatial distribution of microplastic particles were extracted at the same measurement location.

[0240] When using the traditional local volume fraction weighted allocation method, the average root mean square error (RMSE) of the normalized velocity profile for the five operating conditions is 0.118, and the average RMSE of the normalized concentration profile is 0.136. When using the Lagrange-Eulerian mapping method based on volume diffusion and the fluid reverse diffusion method, the average RMSE of the normalized velocity profile is 0.071, and the average RMSE of the normalized concentration profile is 0.082.

[0241] Based on the above results, the model validation and evaluation module retains the Lagrange-Euler mapping method and the fluid anti-diffusion method based on volume diffusion, and marks the traditional local volume fraction weighted allocation method as the comparison calculation method.

[0242] When using the rigid composite particle model to calculate fibrous microplastic particles, the deviation of the simulated deposition centroid position from the experimental deposition centroid position was 12.4%. When using the particle node model to calculate the same fibrous microplastic particles, the deviation of the simulated deposition centroid position from the experimental deposition centroid position was 6.7%.

[0243] The node bending state, number of particle collisions, and particle contact duration output by the particle node model are used to correct particle transport trajectories. The model validation and evaluation module retains the particle node model in calculations for fibrous and fragmented microplastic particles based on the deposition centroid position deviation results.

[0244] Parameter sensitivity analysis was performed by varying the turbidity inlet velocity, initial turbidity concentration, microplastic particle density, microplastic particle aspect ratio, and particle friction properties. Only one parameter was changed in each calculation, while keeping the computational domain, mesh, computation time, and result output location constant.

[0245] As the turbidity inlet velocity increases, the average transport distance of microplastic particles increases, and the time for particles to reach the bed surface for contact is delayed. When the aspect ratio of microplastic particles increases, the rotation amplitude, nodal bending amplitude, and contact duration between fibrous microplastic particles and sediment particles change.

[0246] The statistical results of interparticle force chains include the number of force chains, the direction of the force chains, the duration of the force chains, and the type of particles affected by the force chains. The model validation and evaluation module correlates the statistical results of the force chains with the final deposition location and burial depth of the microplastic particles, forming the calculation results of the collision, friction, deposition, and burial process of microplastic particles driven by turbidity currents.

[0247] Figure 11 The simulation results and experimental results comparison curves were plotted using the same coordinate range, the same measurement location, and the same evolution time. The model validation and evaluation module was based on... Figure 11 Evaluation indices were calculated based on the corresponding flow velocity profile data, concentration profile data, and spatial distribution data of microplastic particles, and then compared with the corresponding validation thresholds.

[0248] During the velocity profile data comparison, the model validation and evaluation module reads both the measured and simulated normalized velocity data corresponding to each normalized height position, and calculates the difference between them at the same normalized height. Similarly, during the concentration profile data comparison, the model validation and evaluation module reads both the measured and simulated normalized concentration data corresponding to each normalized height position, and calculates the difference between them at the same normalized height. (Appendix) Figure 11 The black circular data markers, black square data markers, hollow triangle data markers, and corresponding profile curves together form a comparative relationship between measured and simulated flow rates and concentrations.

[0249] Through the above system structure and method steps, the three-dimensional morphological data of microplastic particles, static water sedimentation data, drag force model parameters, turbidity flow field data, particle motion data, particle contact data, flexible deformation data, sedimentation and burial data, and model verification data are stored in association with particle identification, experimental identification, working condition identification, and calculation time, thereby completing the numerical simulation of the microplastic transport and deposition process in turbidity flow.

Claims

1. A method for simulating microplastic transport and deposition in turbidity streams, characterized in that, Includes the following steps: Three-dimensional morphological data and static water stable sedimentation baseline data of microplastic particles were collected to obtain geometric data, stable sedimentation velocity and morphological characterization parameters of microplastic particles. Based on the stable settling velocity and the morphological characterization parameters, a drag force model of complex-shaped microplastics is constructed to obtain the drag force model parameters. Based on the geometric data of the microplastic particles and the parameters of the drag force model, a turbid fluid domain and a particle domain are established, the fluid phase and particle phase are solved, and fluid field data, particle volume fraction and particle momentum exchange data are obtained by particle volume fraction diffusion mapping and fluid momentum back diffusion processing. Based on the geometric data of the microplastic particles, the fluid field data, the particle volume fraction and the particle momentum exchange data, the fluid action and flexible deformation state of the particles are calculated, as well as the particle contact response is calculated, to obtain the flexible deformation state, deposition location, burial depth and interparticle force chain data. Based on the stable settling velocity, the fluid field data, the flexible deformation state, the deposition location, the burial depth, and the interparticle force chain data, settling benchmark verification, flume condition verification, and parameter sensitivity analysis are performed to form transport-deposition response data.

2. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for collecting the three-dimensional morphology data of microplastic particles are as follows: Microplastic particles were classified and assigned particle labels according to fragmented microplastic particles, fibrous microplastic particles, film-like microplastic particles, and real microplastic samples. Three-dimensional voxel data, three-dimensional point cloud data, or three-dimensional surface mesh data are acquired using an X-ray three-dimensional microscope. After background removal, particle region segmentation, pore filling, surface reconstruction, and coordinate unification, a closed three-dimensional surface is obtained. Based on the closed three-dimensional surface, the major axis, intermediate axis, and minor axis of the fragmented microplastic particles, as well as the axial length and cross-sectional diameter of the fibrous microplastic particles, are determined. The particle volume, actual surface area, equivalent diameter, projected area, equivalent area diameter, and two-dimensional projected profile perimeter are calculated to form the geometric data of the microplastic particles.

3. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for collecting the basic data on static water stability settlement are as follows: Individual microplastic particles are released from the top of the sedimentation column using a particle release component, and sedimentation images are continuously captured to determine the particle center position and particle orientation. A sequence of sedimentation distance and sedimentation time is generated based on the particle center position and collection time; when the change in sedimentation distance per unit time between adjacent time intervals does not exceed the stability threshold, a stable sedimentation interval is determined, and the stable sedimentation velocity is determined by the sedimentation distance and sedimentation time within the stable sedimentation interval. The stability threshold is determined based on the spatial resolution and temporal resolution of the high-speed camera; Based on the geometric data of the microplastic particles, the Aschenbrenner coefficient, Corey coefficient, Janke coefficient, slenderness, flatness, sphericity, roundness, Delino coefficient, and aspect ratio are calculated to form the morphological characterization parameters, which are then associated with the particle identifier and the stable settling velocity and stored.

4. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for constructing a drag force model of complex-shaped microplastics and obtaining the drag force model parameters are as follows: The particle Reynolds number is determined based on the stable settling velocity, particle density, fluid density, hydrodynamic viscosity, and particle characteristic size, wherein the equivalent diameter is used for fragmented microplastic particles, and the characteristic size corresponding to the dragging direction is used for fibrous microplastic particles. The particle Reynolds number, the morphological characterization parameters and the steady settling velocity are grouped according to particle morphology, and nonlinear regression is performed using the Levenburg-Marquardt algorithm to establish fragment drag force model and fiber drag force model. The parameters of the drag force model were verified and calibrated using the stable settling velocity of real microplastic samples.

5. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for establishing the turbid fluid domain and particle domain and solving for the fluid phase and particle phase are as follows: The turbidity fluid domain is discretized using an Eulerian grid, and turbidity inlet, fluid outlet, top boundary, sidewall boundary, and bottom boundary are defined. In the particle domain, sediment particles and microplastic particles are established, and initial position, initial translational velocity, initial angular velocity, initial attitude, particle density, particle size, particle morphology type and contact properties are set. The velocity and pressure fields are solved using the finite volume method and the phase-coupled semi-implicit pressure correlation equation algorithm. The turbulence parameter field is updated using the renormalized group k-ω turbulence model. The particle phase is solved using the discrete element method. The velocity field, pressure field, concentration field, and turbulence parameter field are then determined as the fluid field data.

6. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for particle volume fraction diffusion mapping and fluid momentum reverse diffusion processing are as follows: Determine the fluid grid cell where the center of each particle is located, write the volume occupied by the particle into the corresponding fluid grid cell, and diffuse it to the adjacent fluid grid cells according to the grid adjacency relationship and spatial distance; The particle volume fraction is determined based on the volume occupied by particles in each fluid grid cell and the volume of the fluid grid cell, while keeping the total volume before and after mapping equal for a single particle and all particles. Based on the spatial weight of the volume diffusion process, the particle momentum source term is subjected to fluid momentum reverse diffusion processing to keep the total momentum exchange between the particle phase and the fluid phase unchanged, thus forming the particle momentum exchange data.

7. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for calculating the fluid action and flexible deformation state of the particles are as follows: The fluid velocity, fluid pressure, fluid concentration, and turbulence parameters are read from the fluid field data to obtain the fluid density, and the fluid velocity, fluid pressure, fluid density, fluid concentration, and turbulence parameters are interpolated to the particle location; The drag force of the complex-shaped microplastic drag force model is used to calculate the lift force, pressure gradient force and virtual mass force, and the turbulent dispersion effect is handled according to the particle-vortex interaction time. Fibrous microplastic particles are constructed by connecting multiple spherical cylindrical units, and fragmented and film-shaped microplastic particles are constructed by connecting multiple rounded triangular prism units. Based on the nodal linear elasticity, nodal bending moment, nodal torsional moment and nodal damping, the position and orientation of each connecting unit are updated to obtain the flexible deformation state.

8. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for calculating the particle contact response are as follows: The contact relationships between sediment particles, between sediment particles and microplastic particles, between microplastic particles, and between particles and the substrate were investigated. The normal contact response was calculated using the Hertz spring-damping model, and the tangential contact response was calculated using the Mindlin-Deresiewicz tangential contact model. The particle translational velocity, angular velocity, spatial position, and attitude were updated based on the fluid action, particle contact response, gravity action, and nodal action. The force chain data between particles is obtained based on the contact relationship; the deposition state is determined when the particles are in continuous contact with the substrate and the particle velocity is not greater than the deposition velocity threshold; the burial state is determined when there is sediment covering the particles and the covering thickness reaches the particle burial determination depth; and the deposition location and the burial depth are obtained. The deposition rate threshold and the particle burial determination depth are determined based on the ratio of particle position measurement resolution to particle time step and the minor axis dimension or cross-sectional diameter of the target particle, respectively.

9. The method for simulating microplastic transport and deposition in turbidity streams according to claim 1, characterized in that, The specific steps for the settlement benchmark verification, flume condition verification, and parameter sensitivity analysis are as follows: Establish a static water calculation domain consistent with the static water settlement experiment, compare the simulated stable settlement velocity with the experimental stable settlement velocity, and calculate the mean absolute error, coefficient of determination, and root mean square error. When the mean absolute error is not greater than 1.00 mm / s, the coefficient of determination is not less than 0.90, and the root mean square error is not greater than 1.20 mm / s, the settlement benchmark verification is deemed successful. A numerical flume matching the experimental conditions of the flume model was established. The turbidity velocity profile, turbidity concentration profile, and spatial distribution of microplastic particles were compared at the same measurement location and evolution time. The velocity profile error, concentration profile error, and microplastic spatial distribution error were calculated. By changing the initial conditions of turbidity flow, initial conditions of particles, particle contact properties, and discrete settings of particle nodes, the variable parameter conditions are compared with the baseline conditions to form the transport and deposition response data.

10. A system for simulating microplastic transport and deposition in turbidity streams, characterized in that, A method for simulating microplastic transport and deposition in turbidity streams according to any one of claims 1 to 9, comprising: The sedimentation data acquisition module is used to collect basic data on the static water stable sedimentation of microplastic particles, and obtain the particle center position, particle posture, sedimentation distance, sedimentation time, and stable sedimentation velocity. The morphological parameter construction module is used to collect three-dimensional morphological data of microplastic particles, obtain geometric data of microplastic particles, and calculate morphological characterization parameters based on the geometric data of microplastic particles; the morphological parameter construction module is also used to construct a drag force model of complex-shaped microplastics based on the stable settling velocity and the morphological characterization parameters, and obtain drag force model parameters. The fluid-structure interaction calculation module is used to establish the turbidity fluid domain and particle domain based on the geometric data of the microplastic particles and the drag force model parameters, solve the fluid phase and particle phase, and obtain fluid field data, particle volume fraction and particle momentum exchange data through particle volume fraction diffusion mapping and fluid momentum back diffusion processing. The transport and deposition analysis module is used to calculate the fluid action and flexible deformation state of the particles based on the geometric data of the microplastic particles, the fluid field data, the particle volume fraction and the particle momentum exchange data, as well as to calculate the particle contact response, and obtain the flexible deformation state, deposition location, burial depth and interparticle force chain data. The model validation and evaluation module is used to perform sedimentation benchmark validation, flume condition validation, and parameter sensitivity analysis based on the stable sedimentation velocity, the fluid field data, the flexible deformation state, the deposition location, the burial depth, and the interparticle force chain data, thereby generating transport and deposition response data.

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